Hodgson believes Palace goalkeeper Hennessey will be found "totally innocent" over allegations he made a Nazi salute.
"We are both hoping and confident that charge won't lead to any particular sanctions," said Hodgson.
"We believe he is totally innocent of any charge being made, although we do understand in this current climate that the FA are duty bound to research anything."
Hennessey was in goal for Palace's 2-0 win at FA Cup opponents Doncaster Rovers on Sunday.
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